T. 5 Pythagorean theorem: word problems 37 C Akira takes a rectangular piece of fabric and makes a diagonal cut from one corner to the opposite corner. The cut she makes is 20 centimeters long and the width of the fabric is 16 centimeters. What is the fabric's length? Submit

To solve this problem, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. In Akira's case, the diagonal cut (20 cm) is the hypotenuse, the width (16 cm) is one leg, and the length (which we need to find) is the other leg. So, we set up the equation: \(20^2 = 16^2 + l^2\). This gives us \(400 = 256 + l^2\), leading us to \(l^2 = 144\). Taking the square root, the length of the fabric is 12 cm. The Pythagorean theorem is not just a math class staple but has real-world applications across various fields! Architects, carpenters, and engineers rely on this theorem to ensure their designs and constructions are correct. Whether it's figuring out the height of a building or ensuring that a ramp meets code, this theorem helps in making precise calculations to avoid costly mistakes and keep projects safe and sturdy. So, the next time you're walking by a new building, remember the Pythagorean theorem might be supporting it!